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Overview
This circle boundary layer case
involves a heat source being applied to the inner boundary of
demonstrates the method of manufactured solutions in which an analytical heat source is derived from an analytical expression of the thermal boundary layer. This derived heat source is applied to a vortex flow around a circular annulus of radius r = [ 1 , 2 ]
. The
, and the numerical heat flux at the inner boundary is checked with the analytical heat flux
at the inner boundary
to a specified tolerance. All
boundaries
boundary temperatures are set to
a
the analytical thermal boundary layer
condition which is a function of r and θ. The applied heat source on the inner boundary is a function of r and θ
solution, and the initial condition is set to 1.
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General Case InformationTemperature Distribution:
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Note that the singularity at (θ=0) is disregarded.
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Solver Parameters
Flow parameters:
Vortex Flow
Vx = V∞ sin(θ)
Vy = V∞ cos(θ)
Boundary Condition:
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ν is the non-dimensional viscosity
R=1
c=0.59 (to mimic the real boundary layer)
Heat source on inner radius boundary
S(r,θ)
Non-dimensional viscosity: ν = 10-2
Solver parameters
:
Equation Set: Scalar 2D
Nonlinear Solver: Newton
Basis Type: Hierarchical
Initial/Max CFL: 1030
Target residual: 10-11
Preconditioning:
Type: ILU (Left)
Reordering: MDF
Outer GMRES iterations (# restarts): 20
Inner GMRES iterations (# Krylov vectors): 200
Tested Outputs
L2 error (compared to an exact solution function)
Numerical heat flux on inner boundary
Exact heat flux error on inner boundary Qexact =Image Added
L∞ of the exact heat flux error
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Flow Conditions:
Scalar Convective Diffusion Equation
Boundary conditions:
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Vortex Flow Image Added where Image Added
Boundary Condition: Image Added where Image Added
Derived Heat Source: Image Added where Image Added
Non-dimensional viscosity: Image AddedPicture of Source Boundary
